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Areas of some wellknown figures are given below:
Example.1 A horizontal pipe for carrying floodwater has a diameter of 1 m. When water in it is 10 cm deep then the width of water surface AB is equal to ________ cm.
(1) 10 cm
(2) 25 cm
(3) 60 cm
(4) 70 cm
(5) None
Correct Answer is Option (3).
 Let O be the centre of circle.
 In ΔOAD
⇒ 502 = 402 + x^{2}
⇒ 2500 – 1600 = x^{2}
⇒ x^{2} = 900
⇒ x = 30 ∴ AB = 2x = 60 cm.
Example.2 Area of the shaded region is:
Correct Answer is Option (1).
Length of a Diagonal
 The length of diagonal of a cuboid =
 The length of a diagonal of a cube =
Example.3 An insect is crawling to climb a 20 metre long pipe of diameter 3.5 metres. If the insect take 4 circular rounds to reach the top of the building, then what will be total distance (in nearer metres) traveled by insect to reach the top?
(1) 47 m
(2) 48 m
(3) 49 m
(4) 50 m
 Since the insect is moving in circular way, so it will cover the distance which will be 4 times the distance of the longest side AB of a right angled triangle. In the figure AO is equal to the circumference of the pipe.
AO = πd = = 11m
BO = 5 m
AB = = = 12.08 m Total distance traveled = 12.08 × 4 = 48.32 m
 Hence distance in nearer meters = 48 m
Example.4 The surface area of a cube is 726 sq metres. Find the volume of the cube
(1) 1234 m^{2}
(2) 1431 m^{2}
(3) 1341 m^{3}
(4) 1331 m^{3}
(5) None of these
Correct Answer is Option(4).
 Surface area S = 726 m^{2} Volume V = ?
 In a cube,
 S = 6a^{2} = 726 ⇒ a^{2} = 121 ⇒ a = 11 m
 So, V = a^{3} = 11^{3} = 1331 m^{3}.
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